Head-up display device

ABSTRACT

A head-up display device is improved in performance by a reduction in size and the satisfactory correction of optical aberration. A head-up display device includes a projection optical system that projects an image displayed on an image display surface to a reflective optical surface disposed at a position facing an predetermined observation position of an observer and allows the observer to visually recognize the enlarged image as a virtual image. In a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror having negative power near the optical axis and a second mirror having positive power near the optical axis in this order from the image display surface and Conditional Expressions (1) and (2) are satisfied.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2016-169020, filed on Aug. 31, 2016. Each of the above application(s) is hereby expressly incorporated by reference, in its entirety, into the present application.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The present invention relates to a head-up display device for a moving body, such as an automobile or the like, and more particularly, to a head-up display device for a large vehicle.

2. Description of the Related Art

In the past, a head-up display device has been known as a device that displays information, such as the indication of a direction, calling for attention, and a travel speed, to a driver of an automobile or the like. The head-up display device is to project the virtual image of an image, which is to be displayed, to the reflective optical surface of a front window, a combiner, or the like so that a driver can recognize information required for the driving of an automobile or the like without taking his eyes off from the field of view. JP2013-61554A is proposed as such a head-up display device. JP2013-61554A discloses a head-up display device in which an image forming unit mounted on a vehicle, such as a passenger car, is disposed in front of a driver so that the driver can visually recognize an enlarged virtual image of a two-dimensional image formed on an image display surface by a first mirror, a second mirror, and a reflective optical surface.

SUMMARY OF THE INVENTION

It is desired that the movement of the line of sight of a driver, at the time of confirming information displayed by the head-up display device, is reduced for safety or the prevention of driver's eyestrain in the head-up display device. In order to reduce the movement of the line of sight of a driver, it is preferable that the focal position of the virtual image is distant from the driver as much as possible. The length of an optical path between the image display surface and the reflective optical surface in the head-up display device needs to be long to make this structure.

In recent years, head-up display devices to be mounted on not only a passenger car but also large vehicles, such as a bus, a truck, a ship, and a heavy machine, have been desired to be developed. A space in which the head-up display device can be disposed in the large vehicle is different from that in a passenger car, and the head-up display device can also be disposed on the rear side or lateral side of a driver's seat, on the ceiling, or the like. According to the arrangement, since the length of an optical path between the reflective optical surface, which is disposed in front of an observer, and the image display surface in the head-up display device can be increased, it is easy to make the focal position of the virtual image be distant from the driver.

However, the head-up display device needs to be reduced in size to increase the degree of freedom of arrangement of the head-up display device as described above.

Further, since an improvement in performance is further required for the head-up display device, it is desired that optical aberration is satisfactorily corrected for an improvement in performance.

The invention has been made in consideration of the above-mentioned circumstances, and an object of the invention is to provide a head-up display device that can be improved in performance by a reduction in size and the satisfactory correction of optical aberration.

A head-up display device of the invention comprises a projection optical system that projects an image displayed on an image display surface to a reflective optical surface disposed at a position facing an predetermined observation position of an observer and allows the observer to visually recognize the enlarged image as a virtual image. In a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror having negative power near the optical axis and a second mirror having positive power near the optical axis in this order from the image display surface and Conditional Expressions (1) and (2) are satisfied,

−50<φ₁/|φ₁₂|<−6  (1)

3.5<φ₂/|φ₁₂|<50  (2)

where, φ₁: power of the first mirror near the optical axis,

φ₂: power of the second mirror near the optical axis, and

φ₁₂: power of a combined optical system of the first and second mirrors.

The “eye box” of the invention means a range in which an observer appropriately can observe the virtual image in a state in which the head-up display device is fixed.

Further, the “image display surface” of the invention includes not only the image display surface of an image display element itself but also an image display surface of a diffusion member in a case in which an image displayed on the image display element is temporarily projected to the diffusion member, such as a diffuser or the like, to enlarge the eye box.

It is preferable that the head-up display device of the invention satisfies any one of Conditional Expressions (1-1) to (3-1). As a preferable aspect, the head-up display device of the invention may satisfy any one of Conditional Expressions (1-1) to (3-1) or may satisfy an arbitrary combination thereof,

−35<φ₁/|φ₁₂|<−8  (1-1)

4<φ₂/|φ₁₂|<20  (2-1)

0.2<φ₃/|φ₁₂|<5  (3)

0.4<φ₃/|φ₁₂|<2  (3-1)

where, φ₃: power of the reflective optical surface near the optical axis.

In the head-up display device of the invention, it is preferable that the reflective optical surface has positive power near the optical axis.

Further, in the head-up display device of the invention, it is preferable that an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.

Furthermore, in the head-up display device of the invention, it is more preferable that the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.

In the invention, “movement of the mirror” means a change in the movement of the mirror, such as the movement of the mirror itself, a change in the inclination of the mirror, and the rotation of the mirror about the optical axis.

Moreover, in the head-up display device of the invention, the image may be an image that is formed as an intermediate image on the basis of image information by an optical system.

In this case, the head-up display device may further comprise a diffuser that is provided on the image display surface present at a formation position of the intermediate image.

In the invention, the “projection optical system” means an optical system between the image display surface and the second mirror, and the “optical system” means an optical system that is positioned on the opposite side to the first and second mirrors with the image display surface sandwich therebetween.

The head-up display device of the invention comprises a projection optical system that projects an image displayed on an image display surface to a reflective optical surface disposed at a position facing an predetermined observation position of an observer and allows the observer to visually recognize the enlarged image as a virtual image. Further, in a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror having negative power near the optical axis and a second mirror having positive power near the optical axis in this order from the image display surface and Conditional Expressions (1) and (2) are satisfied. Accordingly, it is possible to obtain the head-up display device that can be improved in performance by a reduction in size and the satisfactory correction of optical aberration.

−50<φ₁/|φ₁₂|<−6  (1)

3.5<φ₂/|φ₁₂|<50  (2)

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a driver's seat of a bus on which a head-up display device according to an embodiment of the invention is mounted.

FIG. 2 is a diagram showing the schematic structure of a head-up display device of Example 1 of the invention seen in an x-axis direction.

FIG. 3 is a diagram showing the schematic structure of the head-up display device of Example 1 of the invention seen in a y-axis direction.

FIG. 4 is a diagram showing the schematic structure of the head-up display device of Example 1 of the invention seen in a z-axis direction.

FIG. 5 is a diagram showing the schematic structure of a head-up display device of Example 2 of the invention seen in the x-axis direction.

FIG. 6 is a diagram showing the schematic structure of the head-up display device of Example 2 of the invention seen in the y-axis direction.

FIG. 7 is a diagram showing the schematic structure of the head-up display device of Example 2 of the invention seen in the z-axis direction.

FIG. 8 is a diagram showing the schematic structure of a head-up display device of Example 3 of the invention seen in the x-axis direction.

FIG. 9 is a diagram showing the schematic structure of the head-up display device of Example 3 of the invention seen in the y-axis direction.

FIG. 10 is a diagram showing the schematic structure of the head-up display device of Example 3 of the invention seen in the z-axis direction.

FIG. 11 is a diagram showing the schematic structure of a head-up display device of Example 4 of the invention seen in the x-axis direction.

FIG. 12 is a diagram showing the schematic structure of the head-up display device of Example 4 of the invention seen in the y-axis direction.

FIG. 13 is a diagram showing the schematic structure of the head-up display device of Example 4 of the invention seen in the z-axis direction.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of the invention will be described in detail below with reference to drawings. FIG. 1 is a schematic diagram of a driver's seat of a bus on which a head-up display device according to an embodiment of the invention is mounted, FIG. 2 is a diagram showing the schematic structure of a head-up display device of Example 1 seen in an X-axis direction, FIG. 3 is a diagram showing the schematic structure of the head-up display device of Example 1 seen in a Y-axis direction, and FIG. 4 is a diagram showing the schematic structure of the head-up display device of Example 1 seen in a Z-axis direction. For convenience′ sake, this embodiment will be described with reference to the drawings of the head-up display device of Example 1, but the same description as the description of this embodiment can be made even in head-up display devices of Examples 2 to 4.

Further, a head-up display device will be described as a head-up display device, which is mounted on a bus, in the embodiment to be described below. However, the invention is not limited to a head-up display device mounted on a bus, and the head-up display device can be mounted on large vehicles, such as a truck, a ship, and a heavy machine or the like.

As shown in FIG. 1, a head-up display device 10 of this embodiment is disposed in an internal space of a bus 11, that is, on the ceiling of the bus 11, on the rear side or lateral side of a driver's seat, or the like; reflects an image representing information, such as travel speed, emitted from the inside of the head-up display device 10 by a combiner (reflective optical surface) 13 standing on the upper surface of a dashboard 12; and enlarges and displays the image as a virtual image 16 on the front side of a observer (driver) P beyond a front window 14.

An image is reflected by the combiner 13 in this embodiment, but the front window 14 may be made as a reflective optical surface and an image may be directly reflected by the front window 14.

As shown in FIGS. 2 to 4, the head-up display device 10 includes a projection optical system 20 including an image display surface 17 that displays an image, a first mirror 18 that has negative power near an optical axis, and a second mirror 19 that has positive power near the optical axis. In this embodiment, an optical path, which extends from the center of the image display surface 17 and reaches a center 15 a of an eye box 15, is referred to as the optical axis. That is, an optical path A that extends from the center of the image display surface 17, is reflected by the combiner 13, and reaches the center 15 a of the eye box 15, and an optical path B that passes through the combiner 13 and reaches the virtual image 16 as shown in FIG. 1 are referred to as the optical axis. In this embodiment, the eye box 15 means a range in which an observer P appropriately can observe the virtual image 16 in a state in which the head-up display device 10 is fixed, and the center 15 a of the eye box 15 means the center of the range in which the observer P can observe the virtual image 16.

The head-up display device 10 is adapted so that display light emitted from the image display surface 17 is reflected by the first and second mirrors 18 and 19 in this order, and reaches the combiner 13. The projection optical system 20, which includes the image display surface 17, the first mirror 18, and the second mirror 19, is provided inside a device housing, and allows the display light of the image to pass through an opening formed on the device housing. The device housing is not shown in FIGS. 2 to 4.

The image, which is displayed on the image display surface 17, may be an image that is formed as an intermediate image on the basis of image information by an optical system (not shown) positioned on the front side of the projection optical system 20, that is, on the opposite side to the first and second mirrors 18 and 19 with the image display surface 17 sandwich therebetween on the optical axis. In this case, a diffuser may be provided on the image display surface 17 that is present at a formation position of the intermediate image, and the range of the eye box 15 can be enlarged according to this aspect.

Since the first mirror 18 has negative power near an optical axis and the second mirror 19 has positive power near the optical axis in the head-up display device 10 of this embodiment, it is possible to suitably set the power of a combined optical system of the first and second mirrors 18 and 19 by preventing the power of the combined optical system of the first and second mirrors 18 and 19 from being excessively increased. Accordingly, it is possible to reduce the size of the projection optical system 20 and to satisfactorily correct the aberration of the projection optical system 20. It is possible to appropriately ensure the length of the optical path between the image display surface 17 and the combiner 13 by preventing the power of the combined optical system of the first and second mirrors 18 and 19 from being excessively increased.

Further, the power of the first and second mirrors 18 and 19 near the optical axis and the power of the combined optical system of the first and second mirrors 18 and 19 are adapted so as to satisfy Conditional Expressions (1) and (2),

−50<φ₁/|φ₁₂|<−6  (1)

3.5<φ₂/|φ₁₂|<50  (2)

where, φ₁: the power of the first mirror 18 near the optical axis,

φ₂: the power of the second mirror 19 near the optical axis, and

φ₁₂: the power of the combined optical system of the first and second mirrors 18 and 19.

Here, Conditional Expressions (1) and (2) will be described in detail. In this embodiment, the shapes of the reflective surfaces of the first and second mirrors 18 and 19 are expressed by Expression (4),

$\begin{matrix} {z = {\frac{c_{\_ k}*\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {C_{\_ k}^{2}*\left( {x^{2} + y^{2}} \right)}}} + {\sum\limits_{i,j}\; {D_{{ij}\_ k}*x^{i}*y^{j}}}}} & (4) \end{matrix}$

where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins,

C_ _(k) : the reciprocal of the radius of curvature, and

D_(ij) _(_) _(k): free-form surface coefficient.

k denotes the number of the mirror and k is in the range of 1 to 3 in this embodiment. Further, each of i and j denotes a positive integer and i and j are in the range of 1 to 8 in this embodiment. Furthermore, *, that is, the asterisk of Expression (4) means multiplication.

The surface shape in an x-z cross-section is expressed by Expression (5) in a case in which y is 0 in Expression (4).

$\begin{matrix} {z = {\frac{c_{\_ k}*x^{2}}{1 + \sqrt{1 - {C_{\_ k}^{2}*x^{2}}}} + {D_{20{\_ k}}*x^{2}} + {D_{30{\_ k}}*x^{3}} + \ldots}} & (5) \end{matrix}$

In a case in which z of Expression (5) is f(x), Expression (6) and Expression (7) are obtained.

$\begin{matrix} {{f^{\prime}(x)} = {\frac{c_{\_ k}*x}{\sqrt{1 - {C_{\_ k}^{2}*x^{2}}}} + {2*D_{20{\_ k}}*x} + {3*D_{30{\_ k}}*x^{2}} + \ldots}} & (6) \\ {{f^{''}(x)} = {\frac{c_{\_ k}}{\sqrt{\left( {1 - {C_{\_ k}^{2}*x^{2}}} \right)^{3}}} + {2*D_{20{\_ k}}} + {6*D_{30{\_ k}}*x} + \ldots}} & (7) \end{matrix}$

Expression (8) is obtained from the Maclaurin series expansion of f(x).

$\begin{matrix} {{f(x)} = {{f(0)} + {\frac{f^{\prime}(0)}{1!}*x} + {\frac{f^{''}(0)}{2!}*x^{2}} + {\frac{f^{\prime''}(0)}{3!}*x^{3}} + \ldots}} & (8) \end{matrix}$

However, since x is very small near the optical axis, Expression (9) is obtained in a case in which Expression (8) is approximated with the ignorance of third- or higher-order terms.

$\begin{matrix} {{f(x)} = {{{f(0)} + {\frac{f^{\prime}(0)}{1!}*x} + {\frac{f^{''}(0)}{2!}*x^{2}}} = {\frac{C_{\_ k} + {2*D_{20{\_ k}}}}{2}*x^{2}}}} & (9) \end{matrix}$

Expression (9) represents that the surface shape in the x-z cross-section corresponds to a paraboloid of which the curvature is C_ _(k) +2*D₂₀ _(_) _(k). Since the power φ of the reflective optical surface is expressed by “φ=−2*(curvature)”, power φ_(x) in the x-z cross-section is expressed by Expression (10).

φ_(x)=−2*(C_ _(k) +2*D ₂₀ _(_) _(k))  (10)

Likewise, power φ_(y), in a y-z cross-section is expressed by Expression (11).

φ_(y)=−2*(C_ _(k) +2*D ₀₂ _(_) _(k))  (11)

An average of φ_(x) and φ_(y) is defined as the power φ_(k) of each mirror by Expression (12).

φ_(k)=−2*(C_ _(k) +D ₂₀ _(_) _(k) +D ₀₂ _(_) _(k))  (12)

The powers φ₁ and φ₂ of the first and second mirrors 18 and 19 near the optical axis are expressed from Expression (12) by Expressions (13) and (14), respectively.

φ₁=−2*(C_ ₁ +D ₂₀ _(_) ₁ +D ₀₂ _(_) ₁)  (13)

φ₂=−2*(C_ ₂ +D ₂₀ _(_) ₂ +D ₀₂ _(_) ₂)  (14)

Further, in a case in which a gap between the first and second mirrors 18 and 19 on the optical axis is denoted by L₂, the power φ₁₂ of the combined optical system of the first and second mirrors 18 and 19 is expressed by Expression (15).

φ₁₂=φ₁+φ₂ −L ₂*φ₁*φ₂  (15)

The values of Conditional Expressions (1) and (2) are calculated using φ₁, φ₂, and φ₁₂ that are defined as described above.

Conditional Expression (1) determines a preferable numerical range of a ratio of the power φ₁ of the first mirror 18 to the absolute value of the power φ₁₂ of the combined optical system of the first and second mirrors 18 and 19. It is possible to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19 and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not smaller than the lower limit of Conditional Expression (1). It is possible to reduce the size of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19 and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not larger than the upper limit of Conditional Expression (1). The projection optical system 20 can have more satisfactory characteristics in a case in which Conditional Expression (1-1) is satisfied.

−35<φ₁/|φ₁₂|<−8  (1-1)

Conditional Expression (2) determines a preferable numerical range of a ratio of the power φ₂ of the second mirror 19 to the absolute value of the power φ₁₂ of the combined optical system of the first and second mirrors 18 and 19. It is possible to reduce the size of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19 and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not smaller than the lower limit of Conditional Expression (2). It is possible to satisfactorily correct the aberration of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19 and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not larger than the upper limit of Conditional Expression (2). The projection optical system 20 can have more satisfactory characteristics in a case in which Conditional Expression (2-1) is satisfied.

4<φ₂/|φ₁₂|<20  (2-1)

It is preferable that the combiner 13 has positive power near the optical axis in the head-up display device 10 of this embodiment. According to this structure, an angle of view (virtual image display size) can be increased.

Further, the power of the combiner 13 near the optical axis and the power of the combined optical system of the first and second mirrors 18 and 19 are adapted so as to satisfy Conditional Expression (3),

0.2<φ₃/|φ₁₂|<5  (3)

where, φ₃: the power of the combiner 13 near the optical axis.

The power φ₃ of the combiner 13 near the optical axis is expressed from Expression (12) by Expression (16).

φ₃=−2*(C_ ₃ +D ₂₀ _(_) ₃ +D ₀₂ _(_) ₃)  (16)

The value of Conditional Expression (3) is calculated using φ₃ that is defined as described above.

Conditional Expression (3) determines a preferable numerical range of a ratio of the power φ₃ of the combiner 13 near the optical axis to the absolute value of the power φ₁₂ of the combined optical system of the first and second mirrors 18 and 19. It is possible to satisfactorily correct the aberration of the projection optical system 20 while reducing the size of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19, the power φ₃ of the combiner 13, and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not smaller than the lower limit of Conditional Expression (3). It is possible to satisfactorily correct the aberration of the projection optical system 20 while reducing the size of the projection optical system 20 by respectively setting the powers φ₁ and φ₂ of the first and second mirrors 18 and 19, the power φ₃ of the combiner 13, and the gap L₂ between the first and second mirrors 18 and 19 on the optical axis so that the ratio is not equal to or not larger than the upper limit of Conditional Expression (3). The projection optical system 20 can have more satisfactory characteristics in a case in which Conditional Expression (3-1) is satisfied.

0.4<φ₃/|φ₁₂|<2  (3-1)

It is preferable that the angle of luminous flux toward the combiner 13 from the projection optical system 20 is made variable by the movement of at least one mirror selected from the first and second mirrors 18 and 19 in the head-up display device 10 of this embodiment. According to this structure, an observer (driver) P can correct the deviation of the angle of luminous flux that is caused by a manufacturing error of the projection optical system 20. The observer (driver) P can correct the deviation of the angle of luminous flux while seeing the virtual image 16 by moving the mirror after the projection optical system 20 is installed.

Further, it is preferable that the angle of luminous flux toward the combiner 13 from the projection optical system 20 is made variable by the movement of the mirror, which is disposed at a position closest to the center 15 a of the eye box 15, of the first and second mirrors 18 and 19 in the head-up display device 10 of this embodiment. According to this structure, the deviation of the angle of luminous flux can be corrected after the projection optical system 20 is installed. Furthermore, since the observer (driver) P can operate the mirror physically closest to a seating position (predetermined observation position), the ease of an operation can be improved.

In this embodiment, for the change of the angle of luminous flux, the mirror may be moved, the inclination of the mirror may be changed, the mirror may be rotated about the optical axis, and the mirror may be moved by a combination thereof.

The head-up display device 10 of this embodiment includes the projection optical system 20 that projects an image displayed on the image display surface 17 to the combiner 13 disposed at a position facing an predetermined observation position of an observer P and allows the observer P to visually recognize the enlarged image as the virtual image 16. In a case in which an optical path, which extends from the center of the image display surface 17 and reaches the center 15 a of the eye box 15, is referred to as the optical axis, the projection optical system 20 includes the first mirror 18 having negative power near the optical axis and the second mirror 19 having positive power near the optical axis in this order from the image display surface 17, and Conditional Expressions (1) and (2) are satisfied. Accordingly, it is possible to obtain the head-up display device that can be improved in performance by a reduction in size and the satisfactory correction of optical aberration.

−50<φ₁/|φ₁₂|<−6  (1)

3.5<φ₂/|φ₁₂|<50  (2)

Next, Examples of numerical values of the head-up display device of the invention will be described. First, a head-up display device of Example 1 will be described.

Table 1 shows the arrangement coordinate data of the respective elements of the head-up display device. Here, combinations of an absolute coordinate system, which uses the center of the image display surface 17 shown in FIGS. 2 to 4 as an origin, and local coordinate systems, which are set on the surfaces of the respective elements, such as the first mirror 18, the second mirror 19, and the combiner 13, will be described.

The local coordinate systems will be set as described below. The origins, an x-axis component vector, a y-axis component vector, and a z-axis component vector of each local coordinate system, are expressed as (x,y,z), (Vx_(x),Vx_(y),Vx_(z)), (Vy_(x),Vy_(y),Vy_(z)), and (Vz_(x),Vz_(y),Vz_(z)) on the absolute coordinate system, respectively. A plane (y-z plane) orthogonal to an x axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to an x axis of the local coordinate system. A plane (x-z plane) orthogonal to a y axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to a y axis of the local coordinate system. A plane (x-y plane) orthogonal to a z axis is used as the reference plane of each element, and a normal vector to each reference plane corresponds to a z axis of the local coordinate system.

Further, each of the first mirror 18, the second mirror 19, and the combiner 13 is a mirror having power, and Table 2 shows data about the shapes of the reflective surfaces of the respective mirrors. The shape of the reflective surface of each mirror is expressed by Expression (4). The first mirror 18 corresponds to a case in which k is 1 in Expression (4), the second mirror 19 corresponds to a case in which k is 2 in Expression (4), and the combiner 13 corresponds to a case in which k is 3 in Expression (4). However, since the respective values of the respective mirrors are written in Table 3, a value of k is not written in Table 3.

$\begin{matrix} {z = {\frac{C_{\_ k}*\left( {x^{2} + y^{2}} \right)}{1 + \sqrt{1 - {C_{\_ k}^{2}*\left( {x^{2} + y^{2}} \right)}}} + {\sum\limits_{i,j}{D_{{ij}\_ k}*x^{i}*y^{j}}}}} & (4) \end{matrix}$

where, x, y, z: coordinates of each surface shape using surface vertexes of image display surface as origins (mm),

C_ _(k) : the reciprocal of the radius of curvature (1/mm), and

D_(ij) _(_) _(k): free-form surface coefficient.

TABLE 1 EXAMPLE 1 COORDINATES OF ORIGINS OF x AXIS OF LOCAL RESPECTIVE SURFACES COORDINATE SYSTEM x y z Vxx Vxy Vxz IMAGE 0.00 0.00 0.00 0.8577 −0.1120 −0.5017 DISPLAY SURFACE FIRST 27.50 −21.25 37.50 0.9872 0.0495 0.1515 MIRROR SECOND 135.00 −76.25 −45.00 −0.8875 0.1602 −0.4321 MIRROR REFLECTIVE 149.36 −545.58 1395.00 0.9793 0.0000 −0.2025 OPTICAL SURFACE CENTER OF −140.00 −226.25 720.00 0.9191 0.0000 −0.3940 EYE BOX VIRTUAL 4146.84 −4957.09 10720.00 1.0000 0.0000 0.0000 IMAGE y AXIS OF LOCAL z AXIS OF LOCAL COORDINATE SYSTEM COORDINATE SYSTEM Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.2247 0.9595 0.1699 0.4623 −0.2585 0.8482 DISPLAY SURFACE FIRST −0.0535 0.9983 0.0223 −0.1502 −0.0301 0.9882 MIRROR SECOND 0.1614 0.9863 0.0342 0.4316 −0.0394 −0.9012 MIRROR REFLECTIVE 0.0731 0.9326 0.3534 0.1888 −0.3608 0.9133 OPTICAL SURFACE CENTER OF 0.1571 0.9171 0.3665 0.3613 −0.3988 0.8429 EYE BOX VIRTUAL 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE 2 EXAMPLE 1 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 4.1406873532E−03 −1.7427295044E−03 −2.0856885808E−04  D₂₀ −7.0488233464E−04   2.1190991218E−05 1.8978155498E−06 D₁₁ 1.1411630764E−03  3.5040269677E−04 2.5245859992E−06 D₀₂ 5.6042869322E−05 −2.1099762426E−04 7.5203038015E−07 D₃₀ 3.6818225575E−06 −2.5327458613E−07 8.2840423822E−09 D₂₁ 7.1122592245E−06 −3.7902591091E−07 −8.1271072949E−09  D₁₂ 9.1490274706E−06 −7.2589872631E−07 −2.1034290263E−08  D₀₃ 7.9794043952E−06 −6.8288685483E−07 1.0861210574E−08 D₄₀ 2.3301920171E−08  2.7160940095E−10 2.1001068129E−10 D₃₁ 1.7945683260E−07  6.3669142339E−11 2.7138288261E−11 D₂₂ 2.2844721053E−07 −3.4289225002E−09 3.8514030439E−10 D₁₃ 1.2538502910E−07  1.5794956869E−09 5.6074317916E−11 D₀₄ 3.4240989884E−08  8.3256471122E−10 −2.6968229274E−11  D₅₀ −1.6819155322E−12  −8.9627172436E−13 1.2528307989E−13 D₄₁ −9.6570600213E−11  −6.2915531917E−13 1.5887622569E−13 D₃₂ −4.9985144694E−11   7.2162596391E−14 7.5376151699E−13 D₂₃ −1.2447402599E−10   1.4357891423E−12 −3.5616569692E−13  D₁₄ 8.2888157099E−12  3.0302400858E−13 −2.4433134595E−13  D₀₅ 1.4610675951E−11 −4.3497161714E−13 4.1992228003E−14 D₆₀ −1.1542437590E−12  −1.1098187483E−14 −3.7810090342E−16  D₅₁ −2.6644627464E−13  −9.6527147573E−15 4.6345482534E−16 D₄₂ 6.0543844242E−12  1.2360927913E−14 −2.3080498215E−15  D₃₃ −5.6078353174E−13  −2.0648914032E−14 9.2628774074E−16 D₂₄ 1.8930334176E−13  1.0575645525E−14 8.9546704699E−16 D₁₅ −3.9021033268E−13  −1.2165325386E−14 −4.7496174966E−16  D₀₆ 2.1959434329E−13  1.1246836668E−15 −4.8129648584E−17  D₇₀ 6.7952593533E−15 −2.7935929700E−18 2.9262339430E−18 D₆₁ −1.3949370552E−14  −8.1539906228E−18 9.3472173294E−19 D₅₂ 1.1613501707E−14 −1.5372507579E−17 2.9344943453E−18 D₄₃ −3.2268514087E−14   2.4915342182E−17 −1.6520447363E−18  D₃₄ −1.8429777118E−14  −2.9909400454E−17 7.0310022010E−18 D₂₅ −5.2177609408E−15   3.7583814363E−17 −2.3923312690E−18  D₁₆ 1.1223628346E−15 −3.7998592057E−17 3.8673228650E−19 D₀₇ 7.9572545230E−16  3.0365240393E−18 7.7715653188E−19 D₈₀ −5.6960769150E−16  −1.5317392634E−19 −1.3903439720E−20  D₇₁ −1.2606207938E−17  −1.2060212413E−20 −5.3437910768E−21  D₆₂ 9.8989355419E−16  7.6115961957E−20 −3.8038403794E−20  D₅₃ −2.8191419311E−16  −1.9000363801E−19 −1.5912852566E−20  D₄₄ 1.4603938257E−16  1.9621169090E−19 2.0007802158E−21 D₃₅ −3.5209822077E−17  −3.3729862552E−19 8.1134632810E−21 D₂₆ 6.7093993797E−17  1.6729368484E−19 −1.9032965278E−21  D₁₇ −2.9675789355E−17   1.4517471581E−19 −1.8039910919E−21  D₀₈ 1.6204566417E−17  1.6237124286E−20 −2.8932163311E−21 

Since symbol and meaning of each data mentioned in the description of Example 1 and a method of describing each data are the same as those in the following examples as long as not particularly stated, the repeated description thereof will be omitted below.

Next, a head-up display device of Example 2 will be described. FIGS. 5 to 7 are diagrams showing the schematic structure of the head-up display device of Example 2. Further, Table 3 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 2, and Table 4 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE 3 EXAMPLE 2 COORDINATES OF ORIGINS OF x AXIS OF LOCAL RESPECTIVE SURFACES COORDINATE SYSTEM x y z Vxx Vxy Vxz IMAGE 0.00 0.00 0.00 0.8398 −0.1947 −0.5068 DISPLAY SURFACE FIRST 22.50 −15.00 45.00 0.9612 −0.1711 0.2165 MIRROR SECOND 145.00 −75.00 −50.00 −0.8900 0.1454 −0.4322 MIRROR REFLECTIVE 154.36 −544.33 1400.00 0.9797 0.0000 −0.2006 OPTICAL SURFACE CENTER OF −135.00 −225.00 725.00 0.9191 0.0000 −0.3940 EYE BOX VIRTUAL 4151.84 −4955.84 10725.00 1.0000 0.0000 0.0000 IMAGE y AXIS OF LOCAL z AXIS OF LOCAL COORDINATE SYSTEM COORDINATE SYSTEM Vyx Vyy Vyz Vzx Vzy Vzz IMAGE 0.2302 0.9731 0.0077 0.4917 −0.1231 0.8620 DISPLAY SURFACE FIRST 0.1781 0.9839 −0.0134 −0.2107 0.0514 0.9762 MIRROR SECOND 0.1446 0.9889 0.0350 0.4324 −0.0314 −0.9011 MIRROR REFLECTIVE 0.0722 0.9330 0.3527 0.1872 −0.3600 0.9140 OPTICAL SURFACE CENTER OF 0.1571 0.9171 0.3665 0.3613 −0.3988 0.8429 EYE BOX VIRTUAL 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE 4 EXAMPLE 2 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C 2.7804357441E−03 −1.3904762082E−03 −2.2787825812E−04  D₂₀ 7.1862827513E−04 −1.4462292880E−04 2.2121830452E−05 D₁₁ 3.9991124479E−04  3.0941074381E−04 2.5422271693E−07 D₀₂ 1.2601197792E−04 −1.5783805113E−04 9.3129565390E−06 D₃₀ −1.4528154513E−05  −8.8484335965E−07 4.1364351554E−09 D₂₁ 7.1341744640E−07 −3.2805874443E−07 −1.8057545611E−09  D₁₂ −6.8568953465E−06  −9.0464946890E−07 −1.5208453715E−08  D₀₃ 4.4433314955E−06 −4.1371719525E−07 6.9869180081E−09 D₄₀ 9.7922736511E−08 −1.2119913743E−09 1.2998611030E−10 D₃₁ 2.1297435564E−08 −1.9200280112E−10 8.4969595109E−11 D₂₂ 7.6262384673E−08 −1.9341511352E−09 2.0855422313E−10 D₁₃ 1.3571986280E−07  7.4761230356E−10 5.7218498519E−11 D₀₄ 1.0901563589E−07 −1.0197192228E−09 1.1328119679E−12 D₅₀ −1.3369320895E−10   9.8488025917E−13 1.2508828140E−14 D₄₁ −2.2682942784E−10  −2.1154072049E−12 3.8416524084E−13 D₃₂ 3.7293922882E−10  3.8775332534E−12 3.8585855436E−13 D₂₃ −1.1188307654E−10   3.4430570884E−15 −7.4866407983E−13  D₁₄ −2.8423883362E−10   4.4392385456E−12 −7.1088686808E−14  D₀₅ 3.6327038178E−11 −1.3553713133E−12 2.0413427329E−14 D₆₀ −3.4811428985E−13  −3.1588912914E−15 −1.9224266946E−17  D₅₁ −5.5765300166E−12  −8.5773953362E−15 −7.2727528921E−16  D₄₂ 4.2685812001E−12  7.2845570166E−15 −1.6247568019E−15  D₃₃ 1.1950140756E−12 −1.7401681977E−14 1.3113382010E−15 D₂₄ 3.1084357231E−12 −1.4574899198E−14 3.5599356519E−15 D₁₅ 8.4801972309E−13  5.8496969723E−15 −8.8238642908E−17  D₀₆ 2.9455771609E−12  1.4392544826E−14 −3.7177637037E−17  D₇₀ 9.9243653361E−15  8.6936640301E−18 −3.8106695518E−19  D₆₁ −3.4583525313E−14  −7.4996995173E−18 −7.6811378903E−19  D₅₂ 1.6091757481E−14  1.0934870590E−17 1.8552354258E−18 D₄₃ −2.9335073114E−15   1.2459629960E−17 2.7152429245E−18 D₃₄ 1.0872188742E−14 −1.3372587896E−17 4.7430353014E−18 D₂₅ −8.6055551052E−15   1.9859915724E−17 2.6511820712E−20 D₁₆ −8.7592126004E−15  −3.3242692439E−17 −1.5477429743E−18  D₀₇ 2.7265428337E−16 −3.5647362380E−18 −1.3626331767E−20  D₈₀ −8.1287167008E−16   7.2053858223E−21 −2.0624580045E−21  D₇₁ −5.3371579209E−17   8.0633884675E−21 2.0471629546E−21 D₆₂ −2.4116982541E−16   6.7027918995E−20 −1.7945386942E−20  D₅₃ 2.0134321856E−16 −1.8208742905E−19 −1.2130074182E−20  D₄₄ 1.9441856819E−16  1.9003343053E−20 −1.4396191579E−20  D₃₅ 1.2315210638E−16 −1.4172881471E−19 −1.1924554048E−20  D₂₆ 1.1177985187E−16 −7.9018917860E−20 1.8234961066E−22 D₁₇ 5.0584219434E−17  1.4264446162E−19 9.4221665457E−21 D₀₈ 1.1342514069E−16  2.6835000369E−20 5.6740699919E−23

Next, a head-up display device of Example 3 will be described. FIGS. 8 to 10 are diagrams showing the schematic structure of the head-up display device of Example 3. Further, Table 5 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 3, and Table 6 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE 5 EXAMPLE 3 COORDINATES OF x AXIS OF LOCAL ORIGINS OF COORDINATE RESPECTIVE SURFACES SYSTEM x y z Vxx Vxy Vxz IMAGE 0.00 0.00 0.00 0.8455 0.0720 −0.5291 DISPLAY SURFACE FIRST 30.00 25.00 47.50 0.9874 0.0000 0.1580 MIRROR SECOND 147.50 80.00 −55.00 −0.9114 0.0000 −0.4114 MIRROR REFLECTIVE 130.09 370.82 1395.00 0.9835 0.0000 −0.1811 OPTICAL SURFACE CENTER OF −135.00 272.50 720.00 0.9308 0.0000 −0.3655 EYE BOX VIRTUAL 3792.26 1729.03 10720.00 1.0000 0.0000 0.0000 IMAGE y AXIS OF LOCAL z AXIS OF LOCAL COORDINATE COORDINATE SYSTEM SYSTEM Vyx Vyy Vyz Vzx Vzy Vzz IMAGE −0.1738 0.9740 −0.1452 0.5049 0.2147 0.8360 DISPLAY SURFACE FIRST 0.0083 0.9986 −0.0517 −0.1578 0.0523 0.9861 MIRROR SECOND −0.0318 0.9970 0.0704 0.4102 0.0772 −0.9087 MIRROR REFLECTIVE −0.0305 0.9857 −0.1658 0.1785 0.1686 0.9694 OPTICAL SURFACE CENTER OF −0.0491 0.9909 −0.1250 0.3622 0.1343 0.9224 EYE BOX VIRTUAL 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000 IMAGE

TABLE 6 EXAMPLE 3 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C  6.4104530561E−04 1.5687956208E−03 −1.7618681455E−04  D₂₀  1.5253690932E−03 −1.6507586959E−03  3.8877275827E−06 D₁₁ −7.8025088141E−04 −1.1656532606E−04  8.2231509723E−07 D₀₂  4.7898324345E−04 −1.4486278638E−03  −1.7027851800E−05  D₃₀ −5.5152686023E−06 −5.3740321051E−07  3.2878105722E−09 D₂₁ −2.5313937935E−06 3.4247070067E−07 −1.7439957144E−08  D₁₂ −1.2205671669E−05 −6.7961827019E−07  −6.5526849956E−09  D₀₃  9.7750915706E−06 −1.1846559594E−07  1.5754454351E−08 D₄₀  7.6010830414E−08 −1.8770593202E−09  2.4917638016E−10 D₃₁  5.9843032420E−08 1.6899436354E−09 1.3112985863E−10 D₂₂ −1.1872109193E−08 −1.9995537219E−09  −1.3794916834E−10  D₁₃  1.1602833529E−07 1.5588015595E−09 6.6599333283E−11 D₀₄ −1.1062281001E−07 1.6345503963E−09 2.3785733903E−10 D₅₀ −8.1135277199E−10 −4.2845924386E−12  5.3092353016E−13 D₄₁ −1.2724980105E−09 −4.2901971487E−14  1.9610328531E−12 D₃₂ −1.0629878227E−10 −3.4605158216E−12  1.3240067624E−12 D₂₃ −1.8993000693E−10 −1.1390122574E−11  2.5187148364E−13 D₁₄  1.9488730065E−09 1.8104775482E−11 −4.0407660590E−13  D₀₅ −1.5640289374E−09 2.8807006420E−11 −8.8264731437E−13  D₆₀  8.8733175825E−12 1.9924898816E−14 −9.2431899670E−15  D₅₁  2.0544907025E−11 −2.3773273092E−14  −5.4678673150E−15  D₄₂ −9.4642308801E−12 3.3895471208E−14 9.3960943057E−15 D₃₃  3.3019741984E−12 −4.2168863432E−14  5.2536798404E−15 D₂₄ −1.0184492237E−12 −1.5591869137E−13  5.9552218249E−15 D₁₅ −7.5242357221E−12 2.5910770593E−15 −6.4650028280E−15  D₀₆  9.9381397588E−12 −3.2261489827E−14  −1.4333355430E−14  D₇₀  2.3249420402E−14 1.3590089254E−16 −8.1614070726E−18  D₆₁ −4.4280725947E−13 2.8878084361E−16 −3.8306336217E−17  D₅₂ −1.1117704298E−13 −2.5033856496E−16  −3.1270794140E−17  D₄₃  2.6629686964E−13 2.9462155178E−16 −1.6615861275E−17  D₃₄  4.6631738873E−14 5.3556679313E−16 9.5434420802E−18 D₂₅ −5.3596479202E−14 6.5233919821E−16 1.9109530760E−17 D₁₆ −1.1068286591E−13 1.3266133701E−16 8.8974507124E−18 D₀₇  7.6555000417E−14 −3.5168448375E−16  9.1462712743E−18 D₈₀ −9.6688752369E−16 −2.4962209447E−19  1.2724760425E−19 D₇₁  3.1333338205E−15 1.6337645511E−18 1.0674408393E−19 D₆₂  1.9099606364E−15 −6.8579906486E−19  −1.2070438243E−19  D₅₃ −1.7010363517E−15 −1.1050392289E−19  −1.5667049090E−19  D₄₄ −8.5736461456E−16 3.5543188330E−18 −1.8013158967E−19  D₃₅ −3.5184493970E−16 4.7196803895E−18 5.9570008407E−20 D₂₆  5.1527107163E−16 7.0138096683E−18 4.4024723999E−20 D₁₇  5.9590292646E−16 3.4635114284E−18 1.1425272030E−19 D₀₈ −5.0074916782E−16 8.4555691111E−19 2.0039901420E−19

Next, a head-up display device of Example 4 will be described. FIGS. 11 to 13 are diagrams showing the schematic structure of the head-up display device of Example 4. Further, Table 7 shows the arrangement coordinate data of the respective elements of the head-up display device of Example 4, and Table 8 shows data about the shapes of the reflective surfaces of the respective mirrors.

TABLE 7 EXAMPLE 4 COORDINATES OF x AXIS OF LOCAL ORIGINS OF COORDINATE RESPECTIVE SURFACES SYSTEM x y z Vxx Vxy Vxz IMAGE 0.00 0.00 0.00 0.9240 0.1039 −0.3681 DISPLAY SURFACE FIRST 22.50 10.00 45.00 0.9766 −0.0406 0.2111 MIRROR SECOND 145.00 55.00 −50.00 −0.8961 −0.0460 −0.4415 MIRROR REFLECTIVE 130.09 338.32 1400.00 0.9833 0.0000 −0.1819 OPTICAL SURFACE CENTER OF −135.00 240.00 725.00 0.9308 0.0000 −0.3655 EYE BOX VIRTUAL 3792.26 1696.53 10725.00 1.0000 0.0000 0.0000 IMAGE y AXIS OF LOCAL z AXIS OF LOCAL COORDINATE COORDINATE SYSTEM SYSTEM Vyx Vyy Vyz Vzx Vzy Vzz IMAGE −0.1298 0.9905 −0.0463 0.3598 0.0905 0.9286 DISPLAY SURFACE FIRST 0.0278 0.9976 0.0631 −0.2131 −0.0558 0.9754 MIRROR SECOND −0.0632 0.9977 0.0243 0.4393 0.0497 −0.8969 MIRROR REFLECTIVE −0.0302 0.9861 −0.1633 0.1794 0.1661 0.9697 OPTICAL SURFACE CENTER OF −0.0491 0.9909 −0.1250 0.3622 0.1343 0.9224 EYE BOX VIRTUAL 0.0000 1.0000 −0.0001 0.0000 0.0001 1.0000 IMAGE

TABLE 8 EXAMPLE 4 REFLECTIVE OPTICAL FIRST MIRROR SECOND MIRROR SURFACE C  3.3901553453E−03 −1.4735575766E−03 −2.1865093056E−04 D₂₀  1.5228350908E−04 −1.2158802961E−04  1.6871882531E−05 D₁₁ −8.8655086403E−05 −1.8705581996E−04 −2.1856597936E−06 D₀₂ −1.9203347568E−05 −1.6602207171E−04  2.0250058661E−06 D₃₀ −1.0181218223E−06 −4.7505008987E−07  9.4113430161E−09 D₂₁ −6.6923515037E−06  3.8598112853E−07  7.0749345292E−09 D₁₂  7.1322085393E−06 −4.2144247016E−07 −1.8023614286E−08 D₀₃ −2.1815074667E−06  3.5842659912E−07 −2.0061092833E−08 D₄₀ −1.4503617228E−08 −1.2595456792E−10  1.3565672617E−10 D₃₁ −5.4241521687E−08  3.8399028909E−10  8.3307407062E−11 D₂₂  1.1681024227E−07 −2.5925664313E−09  4.0404927668E−10 D₁₃ −1.0461747494E−07 −1.1084159024E−09 −9.3143687891E−11 D₀₄  5.8003097372E−08 −4.9201976721E−11 −5.0918008708E−12 D₅₀ −5.0105382823E−10 −2.8347844421E−12  1.8288223128E−14 D₄₁  3.2715652761E−10  2.8113171627E−12 −5.2334609853E−13 D₃₂  1.0570419854E−09  1.2944023590E−12  1.7855607454E−12 D₂₃  1.0002847516E−09 −6.5886632653E−12  1.3185072297E−12 D₁₄ −7.7646193942E−10 −2.8158350133E−12 −2.1218461515E−13 D₀₅ −1.3548306476E−10  5.8713623702E−12 −1.2254672177E−13 D₆₀ −4.7146692372E−12 −6.6368843515E−15  4.0860463430E−16 D₅₁ −6.4319335057E−12  1.2544104519E−15 −2.9169426773E−15 D₄₂  8.5841796031E−12  3.0201528819E−15 −2.5516475474E−15 D₃₃ −7.3767463455E−12  1.3335170605E−14  1.6668147039E−15 D₂₄  4.3087486783E−12  2.8405026641E−15  2.9728347830E−15 D₁₅  2.3694988315E−13  4.6223310562E−15  6.7067892304E−16 D₀₆  2.1188485361E−12  4.8563341890E−15 −1.1922255484E−17 D₇₀  1.1010941100E−14 −3.9859073265E−18  4.0738292671E−19 D₆₁ −6.2361574993E−14  5.7185234561E−18  6.3007890725E−19 D₅₂  5.9646805158E−15 −5.2342388559E−18 −3.2292674674E−18 D₄₃ −4.2657887205E−18 −1.9562878299E−18 −3.4164121736E−18 D₃₄ −6.1009514112E−15 −9.6267922473E−19  4.5740246862E−18 D₂₅ −4.8093185807E−16 −1.6882816588E−17 −9.2936686654E−19 D₁₆ −3.1130488960E−15 −1.0315994688E−17  8.3685902262E−20 D₀₇ −3.6068811633E−15 −7.6677814797E−18 −3.3071397441E−19 D₈₀ −7.5668105744E−16  5.4502586413E−21 −1.1316109881E−21 D₇₁  1.0056742789E−15 −2.2121102549E−20 −4.6745469420E−21 D₆₂ −1.9929984930E−15  1.8559071030E−20 −2.9612496721E−20 D₅₃  2.3533019989E−15  1.6133467720E−20 −4.0628544327E−21 D₄₄ −5.1061285140E−16  4.2267689582E−21 −1.9937012573E−20 D₃₅ −7.1786662119E−18  8.1890564063E−20  8.3308709721E−21 D₂₆  5.0483139891E−16 −2.9706058658E−20  2.7888707791E−21 D₁₇ −1.5708976441E−17  6.9096944674E−20 −8.6525253904E−21 D₀₈  7.5067821428E−17  6.2415707031E−20 −1.2630239265E−22

Values corresponding to Conditional Expressions (1) to (3) of the head-up display devices of Examples 1 to 4 are shown in Table 9.

TABLE 9 VALUES OF CONDITIONAL EXPRESSIONS EXPRESSION NUMBER EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 EXAMPLE 4 C _(—) ₁ 4.1407E−03 2.7804E−03 6.4105E−04 3.3902E−03 C _(—) ₂ −1.7427E−03  −1.3905E−03  1.5688E−03 −1.4736E−03  C _(—) ₃ −2.0857E−04  −2.2788E−04  −1.7619E−04  −2.1865E−04  D₂₀ _(—) ₁ −7.0488E−04  7.1863E−04 1.5254E−03 1.5228E−04 D₂₀ _(—) ₂ 2.1191E−05 −1.4462E−04  −1.6508E−03  −1.2159E−04  D₂₀ _(—) ₃ 1.8978E−06 2.2122E−05 3.8877E−06 1.6872E−05 D₀₂ _(—) ₁ 5.6043E−05 1.2601E−04 4.7898E−04 −1.9203E−05  D₀₂ _(—) ₂ −2.1100E−04  −1.5784E−04  −1.4486E−03  −1.6602E−04  D₀₂ _(—) ₃ 7.5203E−07 9.3130E−06 −1.7028E−05  2.0250E−06 L₁ 51.12790 52.50000 61.49187 51.29571 L₂ 146.24466 166.22650 165.34056 161.41948 L₃ 1514.62168 1524.09324 1478.97832 1477.49453 φ₁ −6.9837E−03  −7.2502E−03  −5.2908E−03  −7.0465E−03  φ₂ 3.8651E−03 3.3859E−03 3.0612E−03 3.5223E−03 φ₃ 4.1184E−04 3.9289E−04 3.7865E−04 3.9951E−04 φ₁₂ 8.2888E−04 2.1627E−04 4.4826E−04 4.8230E−04 (1) φ₁/|φ₁₂| −8.4254219 −33.5239519 −11.8030507 −14.6100975 (2) φ₂/|φ₁₂| 4.6629844 15.6559324 6.8290839 7.3031824 (3) φ₃/|φ₁₂| 0.4968586 1.8166685 0.8447257 0.8283369

It is understood from the above-mentioned data that all the head-up display devices of Examples 1 to 4 are head-up display devices capable of being improved in performance by a reduction in size and the satisfactory correction of optical aberration since satisfying Conditional Expressions (1) to (3).

Here, values corresponding to Conditional Expressions (1) to (3) of the head-up display device disclosed in JP2013-61554A are shown in Table 10 as Comparative Examples.

TABLE 10 RELATED ART EXPRESSION COMPARATIVE COMPARATIVE COMPARATIVE NUMBER EXAMPLE 1 EXAMPLE 2 EXAMPLE 3 C _(—) ₁ 6.4103E−03 4.8248E−03 −4.8249E−03 C _(—) ₂ −3.7037E−03  0.0000E+00  1.0000E+02 C _(—) ₃ 0.0000E+00 −1.5480E−03  −3.0000E+02 D₂₀ _(—) ₁ D₂₀ _(—) ₂ D₂₀ _(—) ₃ D₀₂ _(—) ₁ D₀₂ _(—) ₂ D₀₂ _(—) ₃ L₁ 65.00000 31.00000 42.00000 L₂ 80.00000 92.00000 71.00000 L₃ 120.00000 110.00000 90.00000 φ₁ −1.2821E−02  −9.6496E−03   9.6497E−03 φ₂ 7.4074E−03 0.0000E+00 −2.0000E+02 φ₃ 0.0000E+00 3.0960E−03  6.0000E+02 φ₁₂ 2.1842E−03 −9.6496E−03  −6.2964E+01 (1) φ₁/|φ₁₂| −5.8695652 −1.0000000 0.0001533 (2) φ₂/|φ₁₂| 3.3913043 0.0000000 −3.1764000 (3) φ₃/|φ₁₂| 0.0000000 0.3208411 9.5292001

Since all head-up display devices of Comparative Examples 1 to 3 do not satisfy Conditional Expressions (1) and (2) from the above-mentioned data, the same effects as the effects of the invention cannot be obtained. Further, since the head-up display device of Comparative Example 2 satisfies Conditional Expression (3) but does not satisfy Conditional Expressions (1) and (2), the same effects as the effects of the invention cannot be obtained.

The invention has been described using the embodiment and Examples. However, the invention is not limited to the embodiment and Examples and may have various modifications. For example, the positions and sizes of the respective elements of the head-up display device may have other values without being limited to values that are mentioned in Examples of numerical values.

EXPLANATION OF REFERENCES

-   -   10: head-up display device     -   11: bus     -   12: dashboard     -   13: combiner (reflective optical surface)     -   14: front window     -   15: eye box     -   15 a: center of eye box     -   16: virtual image     -   17: image display surface     -   18: first mirror     -   19: second mirror     -   20: projection optical system     -   P: observer (driver) 

What is claimed is:
 1. A head-up display device comprising: a projection optical system that projects an image displayed on an image display surface to a reflective optical surface disposed at a position facing an predetermined observation position of an observer and allows the observer to visually recognize the enlarged image as a virtual image, wherein in a case in which an optical path, which extends from a center of the image display surface and reaches a center of an eye box, is referred to as an optical axis, the projection optical system includes a first mirror having negative power near the optical axis and a second mirror having positive power near the optical axis in this order from the image display surface and Conditional Expressions (1) and (2) are satisfied, −50<φ₁/|φ₁₂|<−6  (1) 3.5<φ₂/|φ₁₂|<50  (2) where, φ₁: power of the first mirror near the optical axis, φ₂: power of the second mirror near the optical axis, and φ₁₂: power of a combined optical system of the first and second mirrors.
 2. The head-up display device according to claim 1, wherein the reflective optical surface has positive power near the optical axis.
 3. The head-up display device according to claim 1, wherein Conditional Expression (3) is satisfied, 0.2<φ₃/|φ₁₂|<5  (3) where, φ₃: power of the reflective optical surface near the optical axis.
 4. The head-up display device according to claim 2, wherein Conditional Expression (3) is satisfied, 0.2<φ₃/|φ₁₂|<5  (3) where, φ₃: power of the reflective optical surface near the optical axis.
 5. The head-up display device according to claim 1, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.
 6. The head-up display device according to claim 2, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.
 7. The head-up display device according to claim 3, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.
 8. The head-up display device according to claim 4, wherein an angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of at least one mirror selected from the first and second mirrors.
 9. The head-up display device according to claim 1, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 10. The head-up display device according to claim 2, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 11. The head-up display device according to claim 3, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 12. The head-up display device according to claim 4, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 13. The head-up display device according to claim 5, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 14. The head-up display device according to claim 6, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 15. The head-up display device according to claim 7, wherein the angle of luminous flux toward the reflective optical surface from the projection optical system is made variable by movement of the mirror, which is disposed at a position closest to the center of the eye box, of the first and second mirrors.
 16. The head-up display device according to claim 1, wherein the image is an image that is formed as an intermediate image on the basis of image information by an optical system.
 17. The head-up display device according to claim 16, further comprising: a diffuser that is provided on the image display surface present at a formation position of the intermediate image.
 18. The head-up display device according to claim 1, wherein Conditional Expression (1-1) is satisfied. −35<φ₁/|φ₁₂|<−8  (1-1)
 19. The head-up display device according to claim 1, wherein Conditional Expression (2-1) is satisfied. 4<φ₂/|φ₁₂|<20  (2-1)
 20. The head-up display device according to claim 1, wherein Conditional Expression (3-1) is satisfied, 0.4<φ₃/|φ₁₂|<2  (3-1) where, φ₃: power of the reflective optical surface near the optical axis. 